Question: The sum of two numbers is $161$, and their difference is $21$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 161}$ ${x-y = 21}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 182 $ $ x = \dfrac{182}{2} $ ${x = 91}$ Now that you know ${x = 91}$ , plug it back into $ {x+y = 161}$ to find $y$ ${(91)}{ + y = 161}$ ${y = 70}$ You can also plug ${x = 91}$ into $ {x-y = 21}$ and get the same answer for $y$ ${(91)}{ - y = 21}$ ${y = 70}$ Therefore, the larger number is $91$, and the smaller number is $70$.